Active magnetic ranging by wellhead current injection

1. A wellbore ranging method for active electromagnetic ranging between a pair of conductive tubulars comprising: i) a first conductive tubular in a first borehole intersecting an earth formation and electrically connected to a first wellhead and ii) a second conductive tubular in a second borehole in the earth formation and electrically connected to a second wellhead, the method comprising:

generating a depth-dependent current on one conductive tubular of the pair of conductive tubulars and a return current on an other conductive tubular of the pair of conductive tubulars and thereby causing an injection current to flow into the earth formation from the one conductive tubular by:

electrically exciting the first conductive tubular at the first wellhead; and

electrically exciting the second conductive tubular at the second wellhead;

wherein the return current on the other conductive tubular results from the injection current from the one conductive tubular and is received from the earth formation;

making an electric field measurement at a borehole depth in the second borehole using at least one sensor in the second borehole, the electric field measurement indicative of an electric field resulting from exciting the first conductive tubular and the second conductive tubular electrically; and

estimating a relative position of the first conductive tubular with respect to the second conductive tubular using the electric field measurement;

wherein the relative position is estimated using an estimated value of the depth-dependent current at the borehole depth.

2. The method of claim 1 , further comprising at least one of: i) electrically exciting the first conductive tubular at the first wellhead by applying a positive voltage while electrically exciting the second conductive tubular at the second wellhead by applying a negative voltage; and ii) electrically exciting the second conductive tubular at the second wellhead by applying a positive voltage while electrically exciting the first conductive tubular at the first wellhead by applying a negative voltage.

3. The method of claim 1 , further comprising at least one of: i) electrically exciting the first conductive tubular at the first wellhead with a power supply while the second conductive tubular at the second wellhead is grounded; and a) electrically exciting the second conductive tubular at the second wellhead with a power supply while the first conductive tubular at the first wellhead is grounded.

4. The method of claim 1 , further comprising electrically exciting the first conductive tubular and the second conductive tubular at the first wellhead and the second wellhead with an AC power supply.

5. The method of claim 1 , further comprising making a magnetic field measurement and wherein the relative position is estimated using the magnetic field measurement at the borehole depth and the estimated value of the depth-dependent current at the borehole depth.

6. The method of claim 5 , further comprising jointly inverting the magnetic field measurement and the electric field measurement.

7. The method of claim 6 wherein jointly inverting the magnetic field measurement and the electric field measurement comprises performing a constrained inversion.

8. The method of claim 5 , further comprising estimating the value of the depth-dependent current at the borehole depth using a ratio of the electric field measurement and the magnetic field measurement.

9. The method of claim 1 , further comprising obtaining the estimated value of the depth-dependent current at the borehole depth by using a depth-dependent spatial resistivity value.

10. The method of claim 1 , further comprising obtaining the estimated value of the depth-dependent current at the borehole depth by performing a forward modeling of current as a function of depth.

11. The method of claim 1 , further comprising estimating the value of the depth-dependent current at the borehole depth by determining a numerical solution to a differential equation including current as a function of depth.

12. The method of claim 1 wherein the first conductive tubular comprises production casing and the second conductive tubular is part of a drilling assembly.

13. The method of claim 1 wherein the second conductive tubular comprises production casing and the first conductive tubular is part of a drilling assembly.

14. A wellbore ranging method for active electromagnetic ranging between a pair of conductive tubulars comprising: i) a first conductive tubular in a first borehole intersecting an earth formation and electrically connected to a first wellhead and ii) a second conductive tubular in a second borehole in the earth formation and electrically connected to a second wellhead, the method comprising:

generating a depth-dependent current on one conductive tubular of the pair of conductive tubulars and a return current on an other conductive tubular of the pair of conductive tubulars and thereby causing an injection current to flow into the earth formation from the one conductive tubular by:

electrically exciting the first conductive tubular at the first wellhead; and

electrically exciting the second conductive tubular at the second wellhead;

wherein the return current on the other conductive tubular results from the injection current from the one conductive tubular and is received from the earth formation;

making an electromagnetic measurement at a borehole depth in the second borehole using at least one sensor in the second borehole, the electromagnetic measurement indicative an electromagnetic field resulting from exciting the first conductive tubular and the second conductive tubular electrically; and

estimating a relative position of the first conductive tubular with respect to the second conductive tubular using the electromagnetic measurement;

wherein generating the depth-dependent current comprises utilizing time synchronization between the generating of the depth-dependent current and making the electromagnetic measurement at the borehole depth in the second borehole.

15. The method of claim 14 wherein the time synchronization is performed using high precision clocks.

16. The method of claim 14 wherein the time synchronization controls the making of the electromagnetic measurement via phase lock loop (PLL) demodulation.

17. The method of claim 14 wherein the time synchronization is used to measure a magnetic field of the earth while at least one of the injection current and the return current have ceased flowing.

18. A wellbore ranging system for active electromagnetic ranging between a pair of conductive tubulars comprising: i) a first conductive tubular in a first borehole intersecting an earth formation and electrically connected to a first wellhead, and ii) a second conductive tubular in a second borehole in the earth formation and electrically connected to a second wellhead, the system comprising:

an electric excitation unit coupled to the first wellhead and the second wellhead and configured to:

generate a depth-dependent current on one conductive tubular of the pair of conductive tubulars and a return current on an other conductive tubular of the pair of conductive tubulars and thereby causing an injection current to flow into the earth formation from the one conductive tubular by:

electrically exciting the first conductive tubular at the first wellhead; and

electrically exciting the second conductive tubular at the second wellhead, such that the return current on the other conductive tubular results from the injection current from the one conductive tubular and is received from the earth formation;

a bottomhole assembly (BHA) configured to be conveyed into a borehole;

a first sensor disposed on the BHA configured to make electric field measurements at a borehole depth in the second borehole, the electric field measurements indicative of an electric field resulting from exciting the first conductive tubular and the second conductive tubular electrically; and

at least one processor configured to estimate a relative position of the first conductive tubular with respect to the second conductive tubular using the electric field measurements;

wherein the relative position is estimated using an estimated value of the depth-dependent current at the borehole depth.

19. The method of claim 14 , wherein the electromagnetic field measurement comprises a magnetic field measurement and an electric field measurement, wherein estimating the relative position includes jointly inverting the magnetic field measurement and the electric field measurement.

20. The method of claim 19 , wherein jointly inverting the magnetic field measurement and the electric field measurement comprises performing a constrained inversion.